What is the domain of f(x)= 3/(sqrt(x^2-8x+15)) ?

The domain of f(x)= 3/(sqrt(x^2-8x+15)) is x 5

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domain of f(x)= 3/(sqrt(x^2-8x+15))

domain

f (x) = \frac{3}{x ^{2} - 8 x + 15}

x < 3 or x > 5

Interval Notation

(- \infty, 3) \cup (5, \infty)

Solution steps

Find non-negative values for radicals:

x \leq 3 or x \geq 5

Find undefined (singularity) points:

x = 5, x = 3

Combine real regions and undefined points for final function domain

x < 3 or x > 5

f (x) = lo g_{5} (x - 2)

\frac{x ^{3} + 1}{x ^{2}}

f (x) = x + 4 x + 2

f (x) = 4 cos (x)

f (x) = 7 x - 6 x^{2} + 12

What is the domain of f(x)= 3/(sqrt(x^2-8x+15)) ?
The domain of f(x)= 3/(sqrt(x^2-8x+15)) is x<3\lor x>5